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With numerous applications, particularly in fluid dynamics, the semi-Lagrangian approximation scheme is an essential part of the numerical analyst's toolkit. This largely self-contained book provides a framework for the semi-Lagrangian strategy for approximation of hyperbolic PDEs, with a special focus on Hamilton Jacobi equations. The authors provide a rigorous discussion of the theory of viscosity solutions and the concepts underlying the construction and analysis of difference schemes; they then proceed to cover high-order semi-Lagrangian schemes and their applications to problems in fluid...

This volume contains 12 papers dealing with the approximation of first- and second-order problems which arise in many fields of application including optimal control, image processing, geometrical optics and front propagation. Some contributions deal with new algorithms and technical issues related to their implementation. Other contributions are more theoretical, dealing with the convergence of approximation schemes. Many test problems have been examined to evaluate the performances of the algorithms. The volume should attract readers involved in the numerical approximation of differential...